Vanishing Viscosity Limit to Planar Rarefaction Wave with Vacuum for 3D Compressible Navier-Stokes Equations
Year: 2023
Author: Xin-Xiang Bian, Yi Wang, Ling-Ling Xie
Communications in Mathematical Analysis and Applications, Vol. 2 (2023), Iss. 1 : pp. 21–69
Abstract
The vanishing viscosity limit of the three-dimensional (3D) compressible and isentropic Navier-Stokes equations is proved in the case that the corresponding 3D inviscid Euler equations admit a planar rarefaction wave solution connected with vacuum states. Moreover, a uniform convergence rate with respect to the viscosity coefficients is obtained. Compared with previous results on the zero dissipation limit to planar rarefaction wave away from vacuum states [27, 28], the new ingredients and main difficulties come from the degeneracy of vacuum states in the planar rarefaction wave in the multi-dimensional setting. Suitable cut-off techniques and some delicate estimates are needed near the vacuum states. The inviscid decay rate around the planar rarefaction wave with vacuum is determined by the cut-off parameter and the nonlinear advection flux terms of 3D compressible Navier-Stokes equations.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/ 10.4208/cmaa.2022-0020
Communications in Mathematical Analysis and Applications, Vol. 2 (2023), Iss. 1 : pp. 21–69
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 49
Keywords: Compressible Navier-Stokes equations vanishing viscosity limit rarefaction wave vacuum.